Dimensional Characterization of Groundwater Oblique Flow Problems with Heat Transport

Abstract

A dimensional study of two problems in which groundwater flow is oblique has been carried out in order to characterize the vertical profiles of temperature along the domain affected by the flow, determining an input region in which the profiles depend on the horizontal position followed by a region in which profiles only depend on the vertical component of the flow. In the first problem, the horizontal and vertical components of velocity are constant. In the second scenario, the oblique flow of groundwater is generated because in the boundary conditions, the hydraulic potentials present a constant value. From the discriminated dimensional analysis of the mathematical model (governing equations and boundary conditions), the dependencies of the unknowns of greatest interest, characteristic lengths for the development of temperature‐depth profiles, velocity profiles and the temperature field, with the dimensionless groups deduced are established. Once these dependencies have been verified, they are graphically represented by means of curves and surfaces as universal solutions to these problems. Based on these universal solutions an inverse problem protocol for estimating water flows from temperature measurements is proposed. The use of universal graphs of the two proposed scenarios avoids the large number of numerical simulations that this type of problem required.

A Universal Graphical Solution to Calculating Seepage in Excavation of Anisotropic Soils and Non-Limited Scenarios

“…Dimensionless seepage reported by [27] According to the Pi Theorem [28], the group containing the unknowns Q, T * and L * (π 4 , π 5 and π 6 ) can be expressed as a function of the rest (Equations ( 10)-( 12)).…”